Structural Change through Diversi…cation:
A Conceptual Framework
Fidel Perez-Sebastiany
[email protected]
Chris Papageorgiou
[email protected]
Nicola Spatafora
[email protected]
March 2013
Abstract
The structural transformation and the process of diversi…cation are crucial
for economic development. This paper is the …rst to present a conceptual framework in which to investigate the inter-relationship between growth, structural
transformation, and the di¤erent dimensions of diversi…cation. Two new concepts – the variety and quality e¤ects – arise as additional driven forces of the
two phenenomena. Results suggests that sectoral output and consumption shares
may not represent good indicators of a country’s stage along the structural transformation and diversi…cation processes unless we employ hedonic price indices.
Without this correction, input measures show up as better indicators. Our …ndings support the view that concentration in sectors with limited scope for horizontal diversi…cation and quality upgrading, such as primary commodities, can
harm the prospects of growth, and that policy can help to avoid this problem.
y
International Monetary Fund
University of Alicante and University of Hull
1
1
Introduction
There is a consensus that economic development critically involves the process of structural transformation. Kuznets (1973) described this process as the reallocation of
economic activity across agriculture, manufacturing and services. More recently, Herrendorf et al. (2011) has revised the evidence, and surveyed the existing literature that
have tried to understand it. As economies grow, the main pattern that we observe is
a reallocation of labor from agriculture to manufacturing and services, and later on,
from agriculture and manufacturing into services.
At the same time, broad patterns have been uncovered in the relationship between
sectoral or export diversi…cation and the level of per capita income. In particular, Imbs
and Wacziarg (2003) document that higher incomes per capita are associated …rst with
diversi…cation, and then with re-concentration, in production and employment, following a U-shaped pattern across a wide variety of data sources. Klinger and Lederman
(2004) and Cadot et al. (2011) …nd similar results for exports. Cadot et al. (2011) also
…nd that this pattern “. . . is an inherent feature of the economic development process
(rather than a re‡ection of the predominance or not of primary-product exports)”.
The above two processes then represent well established phenomena that characterize economic development. However, while both literatures on structural transformation and diversi…cation have ‡ourished, they have also moved independently of each
other as if there isn’t a close relationship between the two. This is a clear shortcoming
that this paper addresses.
Yet there is a third important phenomenon that surrounds the structural transformation and that have received less attention. Economic development crucially involves
changes not only in the type, but also in the quality of goods produced. Higher quality
varieties of existing products can constitute a way of building on existing comparative
advantage. As Papageorgiou and Spatafora (2012) …nd out, there is a strong positive
correlation between the quality of exported goods –measured by their unit value –and
the level of economic development. East Asia constitutes, for example, a clear case of
economies that have on average bene…ted signi…cantly from quality upgrading.
This paper represents a …rst attempt to build and analyze a conceptual framework in
which to investigate the inter-relationship between growth, structural transformation,
and the di¤erent dimensions of diversi…cation. A main goal is trying to understand the
joint driving forces of all these phenomena. More speci…cally, the proposed in…nite2
horizon setup allows for: …rst, changes in the amount of resources allocated to the
three main aggregate production activities; second, the expansion of the number of
goods produced in each of those sectors; and third, the possibility of improving the
quality of existing types of goods. By incorporating all these elements into a uni…ed
growth model, the paper argues that the structural transformation crucially involves
the process of economic diversi…cation in both its horizontal (number of goods) and
vertical (quality of goods) dimensions, which has been omitted by existing literature.
The novel framework adds to the traditional income and price e¤ects two new forces
that shape the structural transformation: the variety and quality e¤ects. These new
forces run through the consumer’s utility function, and create a dichotomy between the
price of goods and the price of utility. While the former price increases with quality,
the latter falls as the economy diversi…es. This is important because the structural
transformation in more standard models is a¤ected by the goods price, whereas in
our model the price of utility is the one that a¤ects the evolution of the sectoral
consumption shares.
Our …ndings imply that, when we look at standard output measures that do not
take into account quality, the capacity of diversi…cation to accelerate the structural
transformation works mainly through its potential e¤ect on total factor productivity.
The reason is that the new forces that work through the utility side actually cause a
ralentization in the evolution of the sectoral output and consumption shares. However,
we also …nd that this evolution may not be a good indicator of the stage at which a
country is located along the structural transformation, unless we employ hedonic price
indices. Without this correction, input-use measures are preferred.
Results agree with the view that concentration in sectors with limited scope for
horizontal diversi…cation and quality upgrading, such as primary commodities, may
result in less broad-based and sustainable economic growth. Policy can help directly,
subsidizing diversi…cation; or indirectly, by promoting non-primary sectors that are
intensive in inputs that are important in the process of diversi…cation. In the context of the model, policy is justi…ed because the generation of knowledge required to
improve the economy’s degree of diversi…cation is surrounded by important positive
externalities.
We proceed as follows. The next section takes a look at the main empirical regularities that characterize the diversi…cation process across nations. Section 3 introduces the
3
model. In section 4, the forces that drive the structural transformation are analyzed.
Section 5 discusses the policy implications. Section 6 concludes.
2
Facts on Diversi…cation
The stylized facts associated to the structural transformation have been analyzed numerous times, and are well known. Early empirical research on the topic includes
Clark (1957), Kuznets (1957, 1966), and Chenery and Syrquin (1975). These authors
emphasized the declining shares of agricultural production and employment, and the
increasing importance of manufacturing and services. More recently, Maddison (1991)
and Buera and Kaboski (2008), among others, have change slightly this picture, documenting the hump-shaped evolution of the manufacturing labor share; implying that
at more advanced levels of development services adsorb resources from the other two
sectors.
The stylized facts related to diversi…cation are, on the other hand, perhaps less
well known. The rest of the section takes a brief look at the most recent cross-country
evidence. In particular, it takes the evidence provided by Papagoergiou and Spatafora
(2012), and organize it into four empirical regularities related to the relationship between the degree of diversi…cation and income per capita.
We consider two key dimensions of diversi…cation: horizontal and vertical. Horizontal diversi…cation is an increase in the number of product lines exported while vertical
diversi…cation is quality improvement to existing products. The idea is that economic
development is underpinned not just by new products and markets, but also by improvements in the quality of products that have already been produced and exported.
Horizontal diversi…cation is measured by constructing a Theil index (see Appendix
1 for precise de…nition) using as the main data source the updated version of the UN–
NBER dataset, which harmonizes COMTRADE bilateral trade ‡ow data at the 4-digit
SITC (Rev. 1) level. Lower values indicate higher diversi…cation. Vertical diversi…cation, or quality upgrading, is proxied by the unit values of exports calculated from the
bilateral trade values and quantities in the updated UN-NBER dataset. Although unit
values have some drawbacks, they constitute an easily observable approximation for
quality (Hallak, 2006). Individual product unit-values are then normalized by the world
average, and country-average unit values are constructed as a geometric value-weighted
mean of the individual product unit values.
4
We next illustrate the four empirical regularities. Two of them are related to
horizontal diversi…cation, and the other two to the vertical dimension. We follow the
variables over time, and across nations with di¤erent income per capita levels. Figure
1 contains the plots, and is divided in four di¤erent panels, A to D.
Fact 1. Horizontal diversi…cation: U-Shape Cross-Country Relationship
Broad patterns have been uncovered in the relationship between sectoral or export
diversi…cation and the level of per capita income. In particular, Imbs and Wacziarg
(2003) document that higher incomes per capita are associated …rst with diversi…cation,
and then with re-concentration, in production and employment. Speci…cally, various
measures of sectoral labor concentration follow a U-shaped pattern across a wide variety
of data sources: countries …rst diversify, in the sense that labor is spread more equally
across sectors, but there exists, relatively late in the development process, a point at
which they start to specialize again.
Klinger and Lederman (2004) and Cadot et al. (2011) …nd similar results for exports. This general relationship holds true at least until an economy reaches advancedeconomy status (with GDP per capita of $25,000-$30,000; see also Cadot et al., 2011).
The relationship is evident in Panel A of Figure 1, which plots country-year observations, with a lower value of the Theil index signaling higher horizontal diversi…cation.
It also holds true when the …gure is restricted to show the pure cross-sectional or timeseries variation; in the latter case, the dataset’s extended time dimension is critical to
con…rming the relationship.
Fact 2. Horizontal Diversi…cation: Heterogeneity across Regions over Time
There is much heterogeneity in horizontal diversi…cation levels, even after controlling
for income per capita. For an extended period, many LICs, in particular in subSaharan Africa (SSA), enjoyed little success in diversifying their exports even when
controlling for size, and commodity-exporting status (see also IMF, 2012, for the recent
SSA experience with structural transformation). Indeed, Panel B shows that SSA
and Middle East & North Africa (MENA) countries have signi…cantly lower levels
of diversi…cation than Asia and Europe. It also shows that South Asia and SSA’s
diversi…cation took o¤ in the mid-1990s.
5
Figure 1: Stylized Facts on Diversi…cation
Panel A: Diversi…cation and GDP
Panel B: Regional diversi…cation over time
Panel C: Export quality and GDP
Panel D: Export quality across countries
Source: Papageorgiou and Spatafora (2012)
Notes: GDP is in real per capita units; data in Panel C come from the manufacturing sector.
6
Fact 3. Vertical Diversi…cation: Quality Upgrading across Countries
Development and structural transformation crucially involves changes in the quality
levels of goods produced, in addition to those in the product mix. Producing higher
quality varieties of existing products can constitute a way of building on existing comparative advantages. It can boost countries’export revenue potential through the use
of more physical- and human-capital intensive production techniques.1 Yet the potential for quality upgrading, that is, the length of a product’s quality ladder, varies
by product (Khandelwal, 2010; Schott, 2004). Therefore, for LICs at early stages of
development, diversi…cation into products with longer quality ladders may be a necessary …rst step before large gains from quality improvement can be reaped. On the
other hand, LICs’ small economic size and limited potential to exploit economies of
scale may result in a high cost of moving into many new products, making quality
upgrading within existing products all the more important.
Panel C illustrates that unit values in manufacturing are positively correlated with
higher incomes per capita at the country level. The relationship holds both across
all goods, and (even more clearly) within manufactures, which have greater scope for
di¤erentiation. The general relationship also holds true in both the cross-sectional
dimension, and the time-series dimension.
Fact 4. Vertical Diversi…cation: Signi…cant Heterogeneity across Countries
Once again, Panel D shows that there is much heterogeneity in quality levels, even
controlling for income per capita. In particular, SSA stands out as producing relatively
low quality goods. Focusing on the time dimension, for an extended period most LICs
and MICs made little progress in increasing their export quality. Since 1990, that has
started changing, particularly in MICs, in East Asia, and among countries of the exSoviet bloc. However, SSA had been largely excluded from these developments. Only
since 2000 has there been some indication of quality upgrading in SSA.
In summary, this section shows that diversi…cation (both horizontal and vertical)
can be a crucial aspect of the development process. The data reveal that diversi…cation involves signi…cant changes in both the type and quality of goods produced
and exported. However, there are major di¤erences across countries in the degree to
1
Schott (2004) shows that within-product quality di¤erences can be dramatic. For instance, unit
values for cotton shirts imported by the U.S. from Japan are 30 times higher than those from the
Philippines.
7
which they have succeeded in carrying out such economic transformation. Over an
extended period, for example, East Asia has on average been particularly successful in
diversifying its exports, particularly in comparison with sub-Saharan Africa. Much of
the progress has occurred through diversi…cation along the extensive margin, that is,
through entry into completely new products.
3
The Model
The framework that we preset embeds the main features of the diversi…cation process
described above into a structural change setup with agriculture, manufacturing and
services. Households consume products from the three di¤erent sectors, and their
demand functions show both income and price e¤ects.
Firms, in turn, behave as pro…t maximizers, and can allocate resources to three
di¤erent objectives. First, the production of units of existing consumption goods –
the intensive margin. Second, the introduction of new goods – the extensive margin.
Third, the increment of the unit value of products –the quality margin. Di¤erences in
a good’s unit value come from di¤erences in input intensities. Products that are more
physical- and human-capital intensive will provide more value added.
For simplicity, we assume that when a new good and/or a quality upgrade is introduced, the …rm that achieves this success and incurs in the …xed cost enjoys monopoly
pricing just for one period. After that period, any …rm can produce the new good and
the new quality under perfect competition without paying any …xed cost again. Put
di¤erently, the new knowledge that was generated in the previous period spills over all
…rms in the economy.
Before describing the model in more detail, it is worth comparing our approach
regarding the di¤erent margins to the one of more standard structural change setups;
Figure 2 presents an illustration of the arguments. In more standard models, the size of
the extensive margin is …xed: there are three goods, one in each sector. What changes
over time and across countries is the size of the intensive margin in each sector: in
more advanced economies, the relative amount produced of services is larger. In our
framework, the contribution of each sector (e.g., manufacturing) to GDP is decomposed
into three dimensions –the intensive, extensive and quality margins –and all of them
change over time.
8
Figure 2: Di¤erent Margins of the Structural Transformation
3.1
Consumers
The economy populated by families, each composed of a number Lt of in…nitely-lived
agents that grows exogenously at rate n. Each individual is endowed with one unit
of time that is split between schooling and labor. Utility is de…ned over consumption
of agricultural goods (cai ), manufacturing products (cmj ), and services (csv ); all consumption variables are measured in per family-member terms. Goods are weighted by
their quality using the quality index qzx for product zx.
More speci…cally, at time t = 1, a representative family values the discounted stream
of utility
U1 =
1
X
1 1=
ct
1
t
t=1
where
c
1
1=
2 (0; 1) is the time discount factor, and
(1)
;
c
c
> 0 is the inter-temporal elas-
ticity of substitution. The variable ct is a total consumption measure that combines
consumption bundles from the three di¤erent sectors.
Following Dixit and Stiglitz (1977):
ct =
h
a (cat
ca ) 1
1=
where
czt =
+
m (cmt
"N
xt
X
cm ) 1
(qzxt czxt )
1=
1 1=
x=1
9
z
#
+ (1
a
m ) (cst
cs )1
1=
i
1
;
(2)
z
z
1
;
z = a; m; s:
(3)
That is, in each sector z, consumption can choose from Nzt di¤erent goods, whose
aggregation introduces a taste for variety into the utility function.
Equality (2) allows for the possibility of having a minimum consumption level of
agricultural goods per person, ca
0; and a level of manufactures and services that
home production can supply, cz
0 for z = m; s. The parameters
z
> 0 and
> 0 represent the inter- and intra-sector elasticities of substitution between goods,
respectively. We can think that the inter-sectoral level corresponds to goods that
are complements, like food, tools and services. The intra-sector level, on the other
hand, corresponds to products that are substitutes, like apples and oranges, cars and
motorbikes, or theaters and museums. This would mean that
1, whereas
z
> 1;
we impose these bounds hereafter.
In exchange for their e¤ort, workers receive a salary (wt ) per each e¢ ciency unit
provided to the production process. We adopt an Macro-Mincer approach to wage
determination: the e¢ ciency of labor is given by exp( et ); where et is the workers’
average educational attainment, and
is the Mincerian return to schooling.2 However,
agriculture does not need educated workers; put di¤erently, only labor hired by the
non-agriculture sectors can obtain a bene…t from schooling. To maintain this setup
consistent and simple, we suppose that each period people are assigned to the di¤erent
sectors randomly according to the optimal input ratios provided by the solutions to
the …rms’pro…t maximization problems, and can not move among sectors after that.
The budget constraint is then given by:
[fat + fnt exp( et )] wt + bt (1 + rt ) =
Nat
X
pait cait +
i=1
Nmt
X
j=1
pmjt cmjt +
Nst
X
psvt csvt + bt+1 (1 + n);
v=1
(4)
where bt is the stock of assets per family member, rt represents the interest rate, pzx is
the price of good zx, and fat and fnt are the fractions of time allocated to agricultural
and non-agricultural labor, respectively. Notice that then fnt = fmt + fst .
Again for simplicity, we suppose that agents that go to school are subtracted from
non-agricultural-sector labor force. That is, in expression (4), we make fnt = 1
fat
fet ; where fet is the fraction of time that the worker allocates to education. Schooling
2
See, for example, Heckman and Klenow (1997), Hall and Jones (1999), Bils and Klenow (2000),
and Papageorgiou and Perez-Sebastian (2005) for discussions of this approach.
10
time increases the average educations attainment in the economy according to:
et+1 =
fet + et
:
1+n
(5)
Consumers maximize (1) subject to conditions (2) to (5). The solution to this
problem for good zx obtains the following optimality conditions for consumption:
qzxt czxt
=
czt
czt
cz
ct
and
=
ct+1
=
ct
z
Pzt
pzxt =qzxt
Pct
Pzt
z
1 + rt+1
1+n
(6)
;
(7)
;
c
Pct
Pct+1
;
(8)
where the price indices for sector-z goods and total consumption equal
Pzt =
"N
zt
X
pzxt
qzxt
x=1
1
and
Pct =
X
z
z=a;m;e
Pzt1
z
#1
!1
1
z
(9)
;
1
:
(10)
These equations say that the consumer’s problem is solved in layers. Expression
(8) is a standard Ramsey-Keynes intertemporal condition that links present and future
total consumption. Equality (7) represents an inter-sector condition: it de…nes the
relative consumption expenditure in each of the three main sectors as a function of
their relative prices. Finally, condition (6) gives the intra-sector choice as a function
of relative prices and quality.
The other decision that the consumer makes is with respect to education. The
Euler equation for human capital accumulation is given by:
exp [ (et
et+1 )] =
wt+1
1 + fnt+1
:
wt (1 + n) (1 + rt+1 )
(11)
The change in education is then driven by the present value per family member of the
future return to schooling.
11
3.2
The intensive margin
Let Yzx be the amount of consumption good zx produced; and Kzx and Lzx the amounts
of physical capital and labor time used as inputs, respectively. Production technologies for agricultural products (a), manufactures (m) and services (s) are given by the
expression
Yzxt = Bzt kzxt [exp(iz et )lzxt ]1
:
(12)
In the last expression, k and l denote quality-adjusted physical and labor, respectively;
Bzt is a TFP parameter; and iz is an indicator parameter that takes on zero for
agriculture, and on one for the secondary and tertiary activities. Hence, unlike the
other two sectors, agriculture does not employ education as an input. Notice that
to be consistent with the adopted Mincerian approach, human capital is introduced
as exp( et )lzxt . Finally, using results in Herrendof and Valentinyi (2008), production
function (12) assumes that the three sectors display the same physical capital share.
Quality-adjusted inputs are de…ned as:
lzxt =
and
Lzxt
,
dzxt
(13)
Kzxt
;
(14)
dzxt
1 represents the input quality index in the production of good zx. The
kzxt =
where dzx
above equalities allow for improvements in quality through the allocation of additional
units of inputs. They can be also interpreted as implying that each unit of new, more
sophisticated inputs are equivalent to dzxt units of old inputs.
Cost minimization implies that a …rm that wants to choose the optimal amount of
each input faces the following problem:
min
fKzxt ;Lzxt g
fwt exp(iz et )Lzxt + rt Kzxt g subject to (12).
(15)
Its solution provides the FOCs:
rt =
Yzxt
Kzxt
zxt
and
wt =
zxt (1
12
)
;
Yzxt
;
Lzxt
(16)
(17)
where
zxt
is the Lagrangian multiplier for product zx at date t; and
is the depreci-
ation rate of capital.
Equations (16) and (17) obtain the capital-labor ratio for the di¤erent sectors as
Kzxt
=
exp(iz et )Lzxt
wt
:
rt +
1
(18)
Hence, the capital to e¢ cient-labor ratio is the same across sectors, and depends on
input prices.
The variable
zxt
captures the marginal cost in the production of good zx. Com-
bining the above conditions, we obtain that
zxt
dzxt
=
Bzx
rt +
z
1
wt
(19)
:
1
To simplify matters, we now take as numeraire the …rst crop ever cultivated in its
version with quality index da1t = 1. Rede…ning marginal costs relative to the one of
this …rst agricultural product, we can write
zxt (dzxt )
= dzxt
Bat
Bzt
(20)
:
Marginal costs are then a function of the quality level of inputs, and in particular,
increase proportionally with it. We can see as well that
zxt
falls with relative TFP.
It is clear that …rms that produce goods with the same quality within a given sector z
will also face the same marginal costs.
3.3
The quality margin
The quality dimension of the model is inspired on Melitz’s (2003) static output-quality
choice framework, including …xed cost of upgrading quality as in Sutton (1991, 1998),
and assuming that product quality requires input quality as in Kugler and Verhoogen
(2012). Goods- and input-quality indices have been introduced above.
In order to have the necessary information to produce higher quality goods, at least
one …rm needs to invest in generating knowledge about the new product and its market.
This cost –call it Qzx –is …nanced through saving. More speci…cally, the relationship
between product quality, input quality, and quality-upgrade costs is given by:
qzxt+1 = minf z Q'zxt [exp( et )]1
13
'
; dzxt+1 g:
(21)
It is immediate that at the optimum, the LHS and the two terms within brackets must
all be equalized.
Expression (21) says that human capital helps to reduce the cost of product upgrading. This is actually the main role of education in the model. We will assume that
a minimum level of human capital ez is necessary to be able to start moving up the
quality ladder. More speci…cally, if et < ez , qzxt = dzxt = 1 for all x.
Under free entry, …rms will upgrade the product until discounted pro…ts net of
…xed costs equal zero. Recalling that monopoly pricing can only be enforced during
one period, this means that
zxt+1
:
(22)
1 + rt+1
is below that amount, other …rms will have incentives to incur in a higher Qzxt ,
Qzxt =
If Qzxt
achieve a larger quality upgrade, and conquer the market.
To …gure out the value of
zxt ,
we …rst need to know the price that the monopolist
will charge. Without competition, this price will be dictated by the solution to the
problem:
max f
fYzxt g
zxt
zxt ) Yzxt g
= (pzxt
subject to (6).
(23)
Which reduces to choosing a markup (mzxt ) over marginal costs taking into account
the good’s demand function. Problem (23) delivers the well-known pricing rule
pzxt = mzxt
zxt
=
zxt
1
1=
(24)
;
z
where the markup falls with the elasticity of substitution between consumption goods.
However, the price in (24) represents only an upper bound, not necessarily the
monopolist´s optimal choice. The reason is that the highest-quality-good producer
competes with lower quality versions, which de facto impose a price cap to the monopolist.
Lower quality vintages can be sold at a price equal to the marginal cost, clearly below the monopolist’s upper bound. From expression (3), it is immediate that consumers
will prefer the product version that o¤ers the smallest price-quality ratio. Therefore,
employing (21), we can write the condition for the new quality level dzxt to be preferred
to the old one dzxt
1
as follows:
pzxt
qzxt
pzxt
qzxt
1
1
,
mzxt
zxt (dzxt )
dzxt
14
zxt (dzxt 1 )
dzxt
1
:
(25)
Combining (20) and (24), the last inequality implies that
)
(
1
dzxt
z
;
:
mzxt = min
dzxt 1
1
z
(26)
This markup condition says that the consumer will always prefer the highest quality,
provided that
> 1. A value of
larger than one is also necessary to be able to
recover the …xed cost.
Notice that condition (26) provides the perfect competition scenario as a particular
case when no quality upgrade occurs: if dzxt equals dzxt
1
then
zxt
= (mzxt 1)
zxt Yzxt
is zero. As a consequence, using information in (20), we can write the pro…t function
relevant for both competitive structures as:
zxt
= (mzxt
Bat
Bzt
1) dzxt
Yzxt :
(27)
Finally, substituting (12) to (14) and (18) into 27, we can write:
zxt
= (mzxt
1) Bat
wt
rt +
1
exp(iz et )Lzxt
(28)
That is, for a given output level, pro…ts rise with TFP, the size of the market (captured
by Lzxt above), and in non-agriculture also with the educational level.
3.4
The extensive margin
The e¤ects of expanding the number of goods that the economy produces in each
industry is captured, in the model, by the TFP object Bzt . This variable is sectorspeci…c, and equals
Bzt =
with
z
z Nzt ;
(29)
being a parameter a¤ected by factors such as the provision of public infrastruc-
ture or subsidies.
Diversi…cation within sectors wants to be an important aspect of the structural
transformation in our model. In particular, the variable Nzt in expression (29) makes
TFP in sector z depend on the industry’s level of diversi…cation. This is a simple
way to link output growth to the variety-expansion speed. The underlying assumption
is that diversi…cation generates complementarities across goods from the productionside viewpoint, or across the inputs that are needed to produce them. For instance,
15
learning-by-doing can generate spillovers across industries within the same sector, making workers more e¤ective.3
When a …rm wants to produce new goods in sector z, it needs to borrow capital to
…nance the …xed cost Fz . This investment, in turn, increases the number of varieties
in sector z according to the technology
Nzt+1
Nzt =
z Fzt Nzt ,
;
2 (0; 1]:
(30)
We can think that the …xed cost allows learning about how to produce the new good.
If many …rms can carry out this type of investment in each sector, new varieties
will be introduced until pro…ts (
zt )
net of …xed costs become zero. Using expression
(30), the zero-pro…t condition that determines the level of Fzt can be written as
Fzt = (Nzt+1
Nzt )
zt+1
1 + rt+1
In order to choose Fzt , the …rm then needs to know
:
(31)
zt+1 .
For tractability purposes, let us make the following two assumptions. First, new
goods come to life with a quality level equal to the one of the other goods produced by
the …rm. Second, other …rms are able to produce versions of the new good but with
a lower quality. With these two additional restrictions, the pricing problem faced by
a …rm that wants to introduce a new product is exactly the same as in the qualityupgrade decision. Hence, the optimal markup and the pro…t function will be given by
(26) and (27), respectively.
3.5
Market-clearing conditions
For goods markets:
sct Yzxt = czxt Lt ;
(32)
where sct is the consumption share in period t. Condition (32) simply implies that all
families save the same fraction of their income.
In the saving market,
(1
sct )
Nzt
X X
Yzxt = bt+1 Lt+1 ;
(33)
z=a;m;s x=1
3
In agriculture, for example, di¤erent complementarities can arise through crop rotations, and due
to seasonality considerations.
16
and
bt+1 Lt+1 = Kt+1 +
X
Fzt +
z=a;m;s
Nzt
X
Qzxt
x=1
!
De…ning K as the economy’s total physical capital stock, and
(34)
:
as its depreciate at
rate, we can write
Kt+1
Kt = It
Kt ;
(35)
where I is investment in physical capital. Physical capital in the model is then accumulated directly from saving, one-for-one.
For the capital and labor inputs, market clearing requires:
Nzt
X X
Kzxt = Kt ;
(36)
Lzxt = (fat + fnt ) Lt :
(37)
z=a;m;s x=1
Nzt
X X
z=a;m;s x=1
4
Results
We now concentrate on the implications of the model for the process of diversi…cation
and structural transformation. First, we show that diversi…cation in the model is the
engine of growth, and therefore, the force that triggers the structural transformation.
After that, we analyze how diversi…cation shapes the evolution of the sectoral shares
in consumption expenditure.
4.1
Diversi…cation: the engine of growth
To see this, we concentrate on the asymptotic balanced-growth path (ABGP) that the
economic approaches. Over there, the e¤ect of the constant cz becomes negligible. As
the e¤ect of cz vanishes, the intertemporal structure of the consumption-saving decision
gets closer to the one a standard multi-sector growth model.
In particular, using expressions (7) and (10), budget constraint (4) can be written
as
[fat + fnt exp( et )] wt + bt (1 + rt ) = Pct ct + bt+1 (1 + n):
(38)
The schooling level et approaches a constant value. This and market clearing condition
(34) imply that Pct ct , bt , wt , Kt =Lt , Fzt =Lt and Nzt Qzxt =Lt will grow at the same rate
17
along the ABGP. But then, the constant growth rates of Pct and ct will determine the
interest rate; according to (8),
r = Gc1= c GPc
1+n
(39)
1;
where Gx denote the gross growth rate of variable xt along the ABGP.
A constant interest rate, in turn, implies that the capital-output ratio grows at the
same rate as the inverse of the marginal cost, by equation (16). Production function
(12) then says that
) GNz GLzx
=(1
GYzx = GNa
Gdzx
(40)
:
And the FOC for labor, expression (17), that
1=(1
Gw = GN a
)
(41)
:
Because of the constant returns to scale that the output production function displays,
the growth rate (41) also gives the one for GDP per capita. Therefore, in the very long
run, the diversi…cation speed is the engine of output per capita growth.
To …gure out the speed of diversi…cation along the ABGP, we can use the fact that
the growth rate of the wage rate implies that the one of investment in new goods equals
GFz = Gw (1 + n). From this, technology (30) delivers
GNz = (1 + n) 1
=(1
)
(42)
:
Which says that, asymptotically, growth rates across sectors are the same, and determined by the population growth rate.
Regarding input quality, clearing condition (37) implies that the growth rate of the
labor input in sector z is GLzx GNz = 1 + n. Then, technology (21) implies that
h
=(1
Gdz = GNz
)
i'=(
(1 + n)
")
:
(43)
If the speed of diversi…cation is the same across sectors then quality upgrades also
occur at the same rate.
4.2
Diversi…cation and the structural transformation
Before the economy reaches the ABGP, there is a long process of structural change
driven at its core by diversi…cation. Diversi…cation favors the acquisition of knowledge
18
that increases labor productivity. This allows the scape from subsistence, and pushes
the economy towards higher and higher income levels.
In terms of the speci…c forces that move the sectoral shares of consumption expenditure, we can identify at least four – two are standard in the literature, whereas
the other two are new. More speci…cally, the existence of consumption endowments
generate the traditional income e¤ect. There is also a standard price e¤ect caused
by changes in the relative sectoral TFP, although in our model, this last force is a
consequence of the creation of new goods.
The above price e¤ect is related to the variation in the relative price of goods.
However, the relevant price behind consumers’behavior is the one of utility; and this
price does not depend only on the one of goods, but also on the two novel forces that are
liked to utility. In particular, better versions of existing products and the expansion
along the extensive margin make utility cheaper, introducing what we call a quality
e¤ect and a variety e¤ect, respectively.
In equilibrium, these forces do not a¤ect the intra-sector allocation of consumption
expenditure. To see this, notice that all producers in sector z face identical demand
functions and production technologies. Hence, a symmetric general equilibrium exists
in which all …rms in sector z choose the same quality jump, charge the same price,
and sell the same amount of output; that is, mzxt = mzt , pzxt = pzt , qzxt = qzt , and
czxt = czt =qzt Nztz
=(
z
1)
for all x. In this equilibrium, none of the e¤ects described
above will modify the consumption shares within sectors.
They are, however, important to determine sectoral expenditure shares. Let us
then look at each of the four forces in more detail to understand their impact. In the
symmetric equilibrium, using de…nition (9), the aggregate sector-demand function (7)
becomes.
Pzt czt
=
Pct ct
z
"
pzt
1=(
Nzt
z
1
1)
qzt Pct
#1
+
pzt
1=(
Nzt
z
cz
:
1)
qzt Pct ct
(44)
The second summand in the RHS gives the income e¤ect. It arises because the …xed
endowment cz implies the non-homotheticity of the utility function. As a consequence,
sectoral consumption shares can change with the level of income even if relative prices
remain constant; the only thing that needs to change is total consumption, Pct ct .
The e¤ect of the other three forces are given by changes in the price of utility.
1=(
This price corresponds in expression (44) to the ratio pzt =qzt Nzt
19
z
1)
. We see that the
expenditure share in z-products grows with the price-to-quality ratio when sectors are
complementary (
< 1). However, to visualize the precise impact, we need to take
into account that the price of goods are endogenous. More speci…cally, expressions
(20), (21), (26) and (29) imply that
min
pzt
1=(
Nzt
z
1)
qzt
=
(
qzxt
qzxt
(
qzt
1)=
;
1
1)=
1=(
Nzt
z
z
z
1
1)
a Nat
z Nzt
(45)
:
Expressions (44) and (45) imply that the consumption ratio falls with the current
quality index qzxt when the markup equals its ceiling, or with last period’s quality when
the markup does not reach that ceiling. Notice that this is a consequence of
being
larger than one, that is, of quality rising faster than production costs.
1=(
The variety e¤ect is given by the term Nzt
z
1)
, and is linked to the taste for va-
riety shown in the utility function. In the symmetric equilibrium, the price of the con1=(
sumption composite czt is provided by the LHS of expression (45). The term Nzt
z
1)
appears because for a speci…c amount of expenditure in z-goods, the value of the composite rises with the number of types Nzt . As a consequence, the cost of czt falls,
increasing the z-products consumption expenditure. Put di¤erently, z-products in
equilibrium become more attractive as their price per unit of utility declines.
Finally, the price e¤ect, generated from the production side of the economy, is given
by the last term in parenthesis in expression (45). Goods prices are determined by their
relative TFP that in our model is a function of the relative degree of diversi…cation.
Goods that become cheaper experienced an increase of their share in consumption
expenditure.
The evolution of the sectoral consumption shares along the growth path will actually
depend on the relative value of the quality and diversi…cation indices, because total
consumption expenditure is the sum across the three production activities. Taking
this into account, our previous analysis implies that the sectoral consumption share
will decline with the relative quality and diversi…cation levels, as long as sectors are
complementary and products within sectors are substitute.
It is important to notice that the values of these relative levels will move with the
relative size of the sector. This can be deduced from expressions (27), (22) and (32).
Combining them we obtain that relative investment in new goods equals:
Qzt
=
Qat
mzxt 1
mait+1 1
dzxt+1
daxt+1
20
Bat+1
Bzt+1
czt
cat
(46)
Hence, a main determinant of relative investment is the consumption ratio; which from
function (7) depends primarily on the relative weight of sectoral consumption in the
utility function,
z = a.
The same follows for relative diversi…cation from zero-pro…t
conditions (22) and (31); they imply that
Fzt
= Nzt+1 Nzt :
(47)
Qzxt
Let us now summarize the forces that shape the structural transformation in our
model. As usual, the process starts from relatively large and relatively low contributions of agriculture and services, respectively, due to initial endowments. The force
that generates the increasing importance of the tertiary sector and the decline of the
primary one in GDP is the income e¤ect. This is the consequence of a larger weight
of consumption of manufacturing and, especially, services in the utility function. The
other three e¤ects –price, quality and diversi…cation –will, on the other hand, cause a
ralentization of the process. The number of services and their quality will grow faster,
eventually reaching a higher value in services than in manufacturing, and a larger value
in manufacturing than in agriculture. As explained above, this will partially o¤set the
impact of the income e¤ect, making the e¤ect of the structural transformation on consumption shares last longer. In the next section, we argue that this has implications
for measurement, since it can lead to a misleading interpretation of the data.
5
Policy and Measurement Implications
In our setup, both dimensions of diversi…cation are surrounded by externalities that
make the private and social returns di¤er, and provide a role to public intervention.
Among them, we have the ones related to the capacity of diversi…cation to accelerate
the structural transformation through its e¤ect on total factor productivity. This e¤ect
can be due to potential scope economies among goods that increase the productivity
of all inputs. It can be also, in the spirit of Hausmann et al. (2005) and Hausmann
(2011), the consequence of complementarities among a higher and higher diversity of
inputs in the production of more and more sophisticated goods. Even though in our
model the causation from diversi…cation to economic growth remains a black box, the
analyses suggests that this is where policy should put more emphases. In particular,
identifying the mix of goods that can have a higher degree of complementarity, or
21
generate stronger externalities is key to make diversi…cation an important engine of
the structural transformation.
Nevertheless, our results also imply that a faster increase in the share of manufacturing and services does not necessarily imply that the economy is increasing welfare
faster. Most measures of an economy’s sectoral composition are based on the price
of goods. This paper, however, suggests that we should focus on the price of utility.
The reason is that goods quality grows faster than their price. In addition, di¤erent
output bundles that require the same expenditure can have di¤erent utility impact due
to di¤erences in variety and quality. Research should then try to build statistics of the
structural transformation based on hedonic price indices in order to improve the policy
analysis.
Another implication of the model is a consequence of the common features that the
processes of diversi…cation and structural transformation share. In the model, the nonprimary sectors are more intensive in human capital, and so is the quality upgrading
activity. Therefore, policy intended to promote the secondary and tertiary production
activities should have as well a positive impact on vertical diversi…cation.
Education shows up as a potentially important policy target. Policies that increase
the net return to schooling would generate additional accumulation of human capital.
This, in turn, can foster the expansion of manufacturing and services, activities that
in equilibrium have more vertical and horizontal diversi…cation potential. All this is
desirable in the model because knowledge created by variety expansion and quality upgrading are surrounded by positive externalities, making the social return to schooling
larger than the private one. Following the same logic, public capital, although omitted
in our model, is clearly another candidate for policy, as long as manufacturing and
services are more intensive in public infrastructure.
6
Conclusion
Development critically involves several inter-related processes. Among them, the literature has emphasized structural transformation, horizontal diversi…cation, and quality
upgrading. These three processes, however, have been analyzed separately as if they
were not connected. This paper has argued that models that focus exclusively on one of
the above aspects can provide misleading policy conclusions. For this reason, a novel
conceptual framework in which the joint forces of diversi…cation and the structural
22
transformation can be analyzed jointly has been proposed.
The model has shown that what drives the evolution of the sectoral consumption
shares is not the relative price of goods but the price of utility, and that these two prices
will not in general coincide. This is a consequence of the impact that diversi…cation has
on the utility side. On the one hand, the expansion in the number of goods produced
by each of the three main sectors –agriculture, manufacturing, and services –occurs
because there is a taste for variety. On the other, quality provides additional utility to
consumers.
Furthermore, along the structural transformation process, the price of goods grows
whereas the price of utility falls. This and the faster rate of diversi…cation in services
imply that the evolution of the sectoral shares provide a distorted image of the evolution
of the relative utility that consumers obtain from each sector. In this sense, changes in
sectoral consumption shares are not a good indicator of the stage at which countries
lie in the structural transformation process. To improve our information, we need to
build measures based on hedonic price indices.
Another consequence of the price dichotomy is that a faster movement along the
quality margin, even though a group of commodities increasingly adsorbs more resources, will always contribute to make an economy look more diversi…ed when using
output data. Based on this, measures of diversi…cation based on input use are more
accurate.
The main message of our paper for policy is the following. Limited diversi…cation
has been an underlying characteristic of many low-income and developing economies.
Concentration in sectors with limited scope for horizontal diversi…cation and quality
upgrading, such as primary commodities, may result in less broad-based and sustainable economic growth. Policy can help because the generation of knowledge required to
improve the economy’s degree of diversi…cation can be associated to important positive
externalities.
Future work should try to calibrate and evaluate quantitatively the model. The calibration is challenging because it needs to be appropriate for less developed nations;
in this, we could follow Berg et al. (2012). Country heterogeneity is a clear candidate
for the test. As shown for example in Papageorgiou and Spatafora (2012), there are
major di¤erences across regions and countries in the degree to which they have succeeded in diversifying and transforming their economies. The test would then be to
23
quantitatively assess whether the model can reproduce this heterogeneity in growth
and diversi…cation experiences.
The quantitative exercise should also serve to produce more precise policy recommendations. More speci…c policy questions that the model can help answer are, for
example, the following. Are di¤erent policies required to accelerate transformation
and hence growth depending on the level of development? Is basic infrastructure more
important in initial stages of the structural transformation, and education later on to
promote quality upgrading?
Finally, opening the economy to the rest of the world also represents an interesting
extension. Many times the opening of the economy is perceived as a prerequisite for
economic growth. The exploration of new foreign markets and export promotion are
an important part of the economic policy agenda in many nations. The introduction
of international trade would allow the model to contribute to this debate.
24
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26
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27
APPENDIX 1. De…nitions of Main Indices
A. Her…ndahl Index
As a starting point, we measure diversi…cation using the Her…ndahl index. The
value of Her…ndahl index, for any given country i and time period t, equals the sum of
squares of export shares (in total exports), where the summation is across all goods j
in the set Jit of categories which the country exports:
HF Iit =
X
2
Xijt
k2Jit Xikt
P
j2Jit
;
where Xijt equals the value of exports by country i of good j at time t. This is an
inverse measure of diversi…cation which ranges from maximum of 1 (no diversi…cation:
all exports lie in a single category) down to 0 (full diversi…cation: each category contains
a negligible fraction of the country’s exports).
B. Theil Index
We calculate the overall, within, and between Theil indices following the de…nitions
and methods used in Cadot et al. (2011). We …rst create dummy variables to de…ne
each product as “Traditional,”“New,”or “Non-traded.”Traditional products are goods
that were exported at the beginning of the sample, and non-traded goods have zero
exports for the entire sample. Thus, for each country and product, the dummy values
for traditional and non-traded remain constant across all years of our sample. For each
country/year/product group, products classi…ed as “new”must have been non-traded
in at least the two previous years and then exported in the two following years. Thus,
the dummy values for new products may change over time.
The overall Theil index is a sum of the within and between components. The
between Theil index is calculated for each country/year pair as:
TB =
X Nk
k
N
k
ln
k
;
where k represents each group (traditional, new, and non-traded), Nk is the total
number of products exported in each group.
k=
is the relative mean of exports in
each group. The within Theil index for each country/year pair is:
"
#
X Nk
X xi
1
x
i
k
TW =
ln
:
N
Nk i2I k
k
k
k
28
C. Unit Values as a Proxy for Quality Upgrading
The Her…ndahl and Theil indices constitute measures of the extent of diversi…cation across product categories. Consequently, they do not cover quality upgrading,
which describes the average quality within any product category. The only directly
observable measures of quality are unit values of exported products. Quality upgrading is assumed to take place if these unit values increase over time. Unit values are
computed by dividing total export value in a product category by export quantity.
For most SITC 4-digit product categories, there is one individual product unit value
for each exporter.4 Individual product unit-values are then normalized by the world
average, and country-average unit values are constructed as a geometric value-weighted
mean of the individual product unit values.
4
Two or more unit values may exist for a given SITC 4-digit category, if quantities are measured
in two or more di¤erent units (e.g. kilograms and number of units). If this is the case, also trade
values are separately available in the dataset for each unit of measurement, so that e¤ectively two or
more “SITC4-plus” categories are constituted.
29